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lfunc_lfunctions • Show schema
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{'Lhash': '4432925714115735566649195580281', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.866219345307726, -1.565943964343618], 'a4': [0.0, 0.0], 'a5': [-2.06765247432125, -0.7525639554597984], 'a6': [0.0, 0.0], 'a7': [-1.4841326115477873, 2.570593088370652], 'a8': [0.0, 0.0], 'a9': [0.5096496123358006, -2.8903665808152397], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6068630553617312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.332640733581296, -0.4777282425313896]]]], 'bad_primes': [2, 19], 'central_character': '76.9', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '2981534186254107079080089065155', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.866219345307726, 1.565943964343618], [0.520944533000791, -2.9544232590366244]], [[1.0, 0], [2.06765247432125, 0.7525639554597984], [3.83022221559489, 3.2139380484326967]], [[1.0, 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{'__RealLiteral__': 0, 'data': '6.42424493897741305481972712634', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6068630553617312, 'bad_primes': [2, 19], 'central_character': '19.9', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/2/i/a/9/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-76-19.9-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-76-19.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.779014156072745, 'root_angle': 0.09111733402986559, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.49696179161483934918036708375', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4432925714115735566649195580281', 'Lhash_array': ['4432925714115735566649195580281'], 'label': '2-76-19.9-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/2/i/a/9/2'}